Apparatus for forming parabolic surfaces



June 1 1965 N. HOGLUND APPARATUS FOR FORMING PARABOLIC SURFACES Filed May 18, 1961 0 m 0 ll 01 4 Sheets-Sheet 1 a II! III INVENTOR. NILS Husumn June 1, 1965 N. HOGLUND APPARATUS FOR FORMING PARABOLIC SURFACES 4 Sheets-Sheet 2 Filed May 18, 1961 III III 7' 0 F o 60 INVENTOR. I \h1.s Hnswnn W 4770211497 June 1, 1965 N. HOGLUND APPARATUS FOR FORMING PARABOLIC SURFACES 4 Sheets-Sheet 5 Filed May 18. 1961 INVENTOR. NIL 5 Ha BLUND BY Wag ATTdVA/EY June 1, 1965 N. HOGLUND 3,186,268

APPARATUS FOR FORMING PARABOLIC SURFACES Filed May 18, 1961 4 Sheets-Sheet 4 F'.6.' FBZ F mew/N "Ml/E wen-"45a; 7/10: 77/! .sz/z) A7 5 20 4N0 awry 1955x1525 4 64/645004 fir/7. m 4770mm United States Patent A, 3,186,268 7 APPARATUS FUR FQRMING PARABGLIC SURFACES Nils Hoglund, 296 Hartshorn Drive, Short Hills, NJ. Filed May 18, 1961, Ser. No. 111,033 6 Claims. (6]. 82-11) My invention relates to forming apparatus, more particularly to apparatus for forming, by precise machining, surfaces having parabolic transverse sections such, for example, as large parabolic mirrors made of light and thin material and useful as a reflector for radar purposes.

For certain applications, true parabolic mirrors of from inch to 4; inch in thickness of preformed aluminum must be machined to an accuracy of a few thousandths of an inch in a 60 inch diameter in order to produce focal points with no more than A inch scattering of light. The tangent to any point of the curve must be mathematically true within 5 minutes with a finish between 5 and micro-inch.

Conventional apparatus utilizing the usual machine controls or numerical control means are not feasible. In conventional apparatus the cutting or forming tools are mounted on slides which may be assembled in different combinations.

One of the more conventional ways of controlling movement of the slides to determine the path of the tool is by cams of various shapes and forms with which cam followers mounted on the tool slides cooperate. However, inherent errors of tool movement are caused due to inaccuracies in the cams, the cam followers and inaccuracies caused by variations in pressure between the cams and followers, the spring loading devices and other moving parts. While these factors can be tolerated for most applications, they cannot be tolerated where very precise dimensions are essential.

Numerical control machining works on a point-to-point basis rather than in a continuous curve. As a result the tool does not follow a continuous curve but follows a step-by-step path. The resulting tangent from point-topoint would be more than the tolerable 5 minutes and hence not acceptable.

It is therefore an object of my invention to provide an improved apparatus for forming parabolic surfaces in a work piece, more particularly, apparatus for precisely forming parabolic mirrors or reflectors.

A further object of my invention is to provide an improved forming apparatus for finishing parabolic mirrors or reflectors of very thin and very light material to a very high degree of accuracy.

A still further object of my invention is to provide an apparatus of the kind described which eliminates the inaccuracies inherent in apparatus using cams or numerical control for determining the movement of the forming tool.

Apparatus made according to my invention includes a base having mounted thereon a rotatable work supporting member for supporting the mirror or reflector to be worked on. A support bracket is mounted on the base adjacent the rotating work supporting member. The bracket slidably supports a double slide assembly above the Work supporting member, the slide assembly carrying a forming tool. The slide assembly supports the tool for movement transversely and normally of the work supporting member. The slide assembly comprises a first slide movable transversely of the work supporting member, and slidably supports the tool slide for movement normal to the work supporting member. A fixed pulley is supported above the axis of rotation of the work supporting member and a rotatable pulley is supported on the tool slide. One end of a flexible member is fixed "ice to the first slide and the other end of the member is fixed to the fixed pulley and has a wrapped engagement therewith. An intermediate portion of the member is in wrapped engagement with the rotatable pulley. As will be described, when the first slide is moved back and forth transversely of the work piece, the tool slide and tool are caused to follow very accurately a parabolic path. The apparatus has means for changing the eccentricity of the parabolic path traced by the tool.

In the drawings:

FIGS. 1 and 2 are diagrams showing the mathematical principles utilized in apparatus employing my invention;

FIG. 3 is a diagram showing the extension of the mathematical principles of FIGS. 1 and 2 to mechanical elements used in apparatus employing my invention;

FIG. 4 is a perspective View of an apparatus made according to my invention and employing the mathematical principles and mechanical elements of FIGS. 1 to 3, inclusive;

FIG. 5 is a schematic diagram of the apparatus shown in FIG. 4 illustrating movement of the slides and tools;

FIGS. 6 and 7 illustrate the change in the path of the tool when certain changes are made in the apparatus disclosed, and

FIG. 8 is an elevation of a pulley of decreasing radius in a counterclockwise direction.

In analyzing the problem, I made the following analysrs:

The definition of a parabola is a locus of points which are equidistant from a given point and a given straight line. FIGURE 1 shows the construction of a parabola according to this definition.

Point X and a straight line Z are equidistant from parabola V; therefore point Y is half the distance along a perpendicular line to Z, that is, from X to Z. At point Y, the a distance from the straight line Z to Y and the straight line a from Y are of equal lengths. This also applies to the length of the lines a and a at points 'YI! Y!!! Referring to FIGURE 2, point X and line Z are represented in the same manner as in FIGURE 1. A line W parallel with line Z is added. As W and Z are parallel, all lines perpendicular to Z between lines Z and W will be of equal lengths; therefore, the sum of a and b and the sum of a and b and the sum of a and b are all equal. It therefore follows that the distance O'YX equals in length OYX; and also equals O"YX, all equals to OY plus YX.

Referring to FIGURE 3, pulleys are placed with their axis of rotation at Y, Y, Y and Y, the pulleys having their center lines coinciding with points Y, Y, Y and Y. Point X is shown as being the focal point of the parabola with a pulley having its center at the focal point. A steel band S held at T is shown wrapped around the pulley at Y and is also wrapped around a stationary non-turning pulley fixed at focal point X and having a radius R. All pulleys have the same radius R.

As point T, the movable end of the tape, is moved to T and Y at the same time is moved to the new location at Y, always assuming that the tape to the left of the pulley remains vertical or normal to line Z, a certain amount of the steel band is unwrapped on the pulley at Y, equivalent to the amount of angle [3' times R (the radius of the pulley). However, an equivalent amount is wrapped around the periphery of the pulley at the focal point X equivalent to R times fi'. There is therefore no change in the overall length of the steel band. It is obvious therefore that as long as the pulley at the focal point and movable pulley at Y are of equivalent diameter, point Y will travel along a true parabolic curve.

The length of the active steel band at point Y is equal to b plus a plus R11- radians. At point Y, the steel band 3 is equal to a plus b and the wrap-around of the steel band at Y has been reduced to (1r/3')R. The wraparound X has been added on by ,B'R. This mathematical relationship is utilized in the apparatus made according to my invention and shown in FIGURE 4.

Referring to FIG. 4, apparatus made according to my invention includes a base 2%) having rotatably supported thereon a drum-like Work supporting member 21 which can be rotatably supported and driven in any suitable manner. A work piece in the form of a preformed parabolic mirror or reflector 22 is fixed to the supporting member during forming operations.

The slide assembly which supports the forming tool includes a supporting bracket 25 fixed to the base 20 and has transversely mounted thereon at the top thereof the elongated slide guide 26 which has one end fixed to bracket 25 and its other end fixed to a frame 27 of more or less tripod shape. This frame 27 mounted on base 20 will further be referred to later. The slide guide 26 is mounted off center with respect to the axis of rotation of the member 21.

The slide assembly further includes a first slide 30 mounted on slide guide 26 by means of a pair of ball bearing assemblies 31 only one of which can be seen. Slide 30 is provided with a transversely positioned slide support 32 supporting a second or tool slide 33, by means of slide guides 34 and ball bearing assemblies 35. Slide 30 is moved along the guide 26 by means of the nut 36 secured to slide 30 and screw 37 rotatably supported at one end in the bracket 38 mounted on slide guide 26. Screw 37 is in turn driven by the gear 39 and worm gear 40 driven by spindle or shaft 40' by any suitable means.

The second or tool slide 33 has mounted at one end, the lower end, the tool assembly 41 carrying the forming tool 42. Also mounted on the tool slide 33 is preferably a rotatable pulley 43. In some instances this could be a fixed member having a curved surface including, for example, 180 degree cam surface. As described above, the tool slide 33 moves normally of the work piece 22. As will be explained, as slide 30 moves transversely of the work piece 22, the tool slide 33 moves normally of the work piece so that the tool 42 follows a path describing an arc. The slide 33 may be biased downwardly by several methods, for example, by gravity, spring means or hydraulic or air pressure.

To cause movement of the tool 42 along a parabolic path, I provide a bracket 45 on which is supported the pulley 46 fixed against rotation. A flexible cable 47, preferably in the form of a narrow steel band, has one end 47' fixed to the adjustable slide 48 mounted on slide 30 and its other end 47 fixed to pulley 46, the cable being in wrapped engagement with the pulley 46 to its fixed point. An intermediate portion of the cable 47 is in wrapped engagement with the rotatable pulley 43.

Since the slide 33 (see FIGS. 4 and is placed so that point Y is perpendicularly below point 0, it is obvious that the distance between Y and X can be changed, that is, shortened or lengthened by changing the position of point 47. Therefore, to change the eccentricity of the parabolic path followed by the tool 42, the slide 43, to which one end of the cable 47 is fixed, is made adjustable on the slide support 32. Slide 48 is provided with an adjusting screw 59 attached thereto by nut 51, screw 59 being rotatably supported on slide support 32 by bracket 52. By turning screw 50, the position of slide 48 and point 47 can be changed.

This change is illustrated by the diagrams shown in FIGS. 6 and 7. Moving point 47 up changes the shape of the parabola from that shown in FIG. 6 to that shown in FIG. 7.

In some applications, extreme accuracy is required. Since the cutting surface of the cutting tool is curved, even though of small dimension, the cutting point on the tool changes as the tool follows the parabolic path.

At its left or upper position, the cutting point is to the left of the vertical center line of the cutting tool. As the tool moves to its central or lowermost position, the cutting point shifts to the lower end of the cutting tool, that is, to the vertical center line. In other words, the cutting point on the tool moves counterclockwise. To compensate for this, the path of the cutter is modified as the tool moves to the right so that the cutting point will fo1- low a true parabolic path. One method of doing this is to shape the surface of the fixed pulley 46 so that its radius is decreased counterclockwise, as will be exemplified by the showing of FIG. 8 of the drawings.

What is claimed is:

1. Apparatus for forming dish-shaped surfaces of parabolic cross section including a base, a rotatable work supporting member on said base, a support member on said base, a slide guide mounted on said support member and extending over said work supporting member, a first slide on said slide guide and movable transversely of said work supporting member, a second slide mounted on said first slide and movable normally of said work supporting memher, a tool on said second slide, a second support on said base, a fixed pulley mounted on said second support and having its axis positioned above the axis of rotation of said rotatable work supporting member, a rotatable pulley mounted on said second slide, a flexible cable having one end fixed to said first slide and its other end to said fixed pulley, and having a wrapping engagement with said fixed pulley, an intermediate portion of said flexible cable having a wrapping engagement with said rotatable pulley, means for moving said first slide whereby said second slide moves transversely and normally of said work supporting member along the path of a parabola, said fixed pulley having a decreasing radius.

2. Apparatus for forming disked surfaces of parabolic cross section including a base, a rotatable work supporting member on said base, a support member on said base, a slide guide mounted on said support member and extending over said work supporting member, a first slide on said slide guide and movable transversely of said work supporting member, a second slide mounted on said first slide and movable normally of said work supporting member, a tool on said second slide, a second support on said base, a fixed pulley mounted on said second support, a rotatable pulley mounted on said second slide, a flexible cable having one end fixed to said first slide and its other end to said fixed pulley, and having a wrapping engagement with said fixed pulley, an intermediate portion of said flexible cable having a wrapping engagement with said rotatable pulley, and means for moving said first slide whereby said second slide moves transversely and normally of said work supporting member along the path of a parabola, said fixed pulley having a decreasing radius.

3. Apparatus for forming dish-shaped surfaces of parabolic cross section including a base, a rotatable work supporting member on said base, a support member on said base, a slide guide mounted on said support member and extending over said work supporting member, a first slide on said slide guide and movable transversely of said work supporting member, a second slide mounted on said first slide and movable normally of said work supporting member, a tool on said second slide, a second support on said base, a fixed member having a curved surface mounted on said second support, a rotatable pulley mounted on said second slide, a slidable member on said first slide, a flexible cable having one end fixed to said slidable member and its. other end to said fixed member having a curved surface, and having a wrapping engagement with the curved surface thereof, said flexible cable having a wrapping engagement with said rotatable pulley, means for biasing said second slide toward said work supporting member, means for moving said first slide whereby said second slide moves transversely and normally of said work supporting member along the path of a parabola, and ad justing means interconnecting said slidable member and first slide for varying the position of the end of said flexible cable fixed to said slidable member.

4. Apparatus for forming dish-shaped surfaces of parabolic cross section including a base, a rotatable work supporting member on said base, a support member on said base, a slide guide mounted on said support member and extending over said work supporting member, a first slide on said slide guide and movable transversely of said Work supporting member, a second slide mounted on said first slide and movable normally of said work supporting member, a tool on said second slide, a second support on said base, a fixed member having a curved surface mounted on said second support, .a rotatable pulley mounted on said second slide, a slidable member on said first slide, a flexible cable having one end fixed to said slidable member and its other end to said fixed member having a curved surface, and having a wrapping engagement with the curved surface thereof, said flexible cable having a wrapping engagement with said rotatable pulley, means for biasing said second slide toward said work supporting member, means for moving said first slide whereby said second slide moves transversely and normally of said work supporting member along the path of a parabola, and means connected to said slidable member for varying the position of the end of said flexible cable connected to said first slide, said fixed member having a curved surface of decreasing radius.

5. Apparatus for forming dish-shaped surfaces of parabolic cross section including a base, a rotatable work supporting member on said base, a supporting bracket on said base, a slide guide secured at one end to said bracket, a first slide slidably mounted on said slide guide, a second slide slidably mounted on said first slide and movable normally of said work supporting member, a frame mounted on said base, a fixed member having a curved surface mounted on said frame, a rotatable pulley mounted on said sec-nd slide, a slidable member on said first slide, a flexible cable having one end fixed to said slidable member and its other end to said fixed member having a curved surface and having a wrapping engagement with the curved surface thereof, said cable having a wrapping engagement with said pulley, means for biasing said second slide toward said work supporting member, means for moving said first slide whereby said second slide moves transversely and normally of said work supporting member along the path of a parabola, and means threadedly interconnecting said slidable member and first slide for varying the position of the end of said flexible cable connected to said slidable member.

6. Apparatus for forming dish-shaped surfaces of parabolic cross section including a base, a rotatable work supporting member on said base, a supporting bracket on said base, a slide guide secured at one end to said bracket, a first slide slidably mounted on said slide guide, a second slide slidably mounted on said first slide and movable normally of said work supporting member, a frame mounted on said base, a fixed member having a curved surface of progressively decreasing radius mounted on said frame, a rotatable pulley mounted on said second slide, a slidable member on said first slide, a flexible cable having one end fixed to said slidable member and its other end to said fixed member having a curved surface and having a wrap ping engagement with the curved surface thereof, said cable having a wrapping engagement with said pulley, means for biasing said second slide toward said work supporting member, means for moving said first slide whereby said second slide moves transversely and normally of said work supporting member along the path of a parabola responsive to the action of said cable relative to said pulley and curved surface, and means connected to said slidable member for varying the position of the end of said flexible cable connected to said first slide.

References Cited by the Examiner UNITED STATES PATENTS 537,126 4/95 Schuckert et al. 51--100 WILLIAM W. DYER, JR., Primary Examiner.

RICHARD H. EANES, JR., Examiner. 

1. APPARATUS FOR FORMING DISH-SHAPED SURFACES OF PARABOLIC CROSS SECTION INCLUDING A BASE, A ROTATABLE WORK SUPPORTING MEMBER ON SAID BASE, A SUPPORT MEMBER ON SAID BASE, A SLIDE GUIDE MOUNTED ON SAID SUPPORT MEMBER AND EXTENDING OVER SAID WORK SUPPORTING MEMBER, A FIRST SLIDE ON SAID SLIDE GUIDE AND MOVABLE TRANSVERSELY OF SAID WORK SUPPORTING MEMBER, A SECOND SLIDE MOUNTED ON SAID FIRST SLIDE AND MOVABLE NORMALLY OF SAID WORK SUPPORTING MEMBER, A TOOL ON SAID SECOND SLIDE, A SECOND SUPPORT ON SAID BASE, A FIXED PULLEY MOUNTED ON SAID SECOND SUPPORT AND HAVING ITS AXIS POSITIONED ABOVE THE AXIS OF ROTATION OF SAID ROTATABLE WORK SUPPORTING MEMBER, A ROTATABLE PULLEY MOUNTED ON SAID SECOND SLIDE, A FLEXIBLE CABLE HAVING ONE END FIXED TO SAID FIRST SLIDE AND ITS OTHER END TO SAID FIXED PULLEY, AND HAVING A WRAPPING ENGAGEMENT WITH SAID FIXED PULLEY, AN INTERMEDIATE PORTION OF SAID FLEXIBLE CABLE HAVING A WRAPPING ENGAGEMENT WITH SAID ROTATABLE PULLEY, MEANS FOR MOVING SAID FIRST SLIDE WHEREBY SAID SECOND SLIDE MOVES TRANSVERSELY AND NORMALLY OF SAID WORK SUPPORTING MEMBER ALONG THE PATH OF A PARABOLA, SAID FIXED PULLEY HAVING A DECREASING RADIUS. 